That is, the Lorentz transformation applies to [itex]\Delta x[/itex] and [itex]\Delta t[/itex] just as it does to x and t, because the transformation is linear.

I'm always sending beginners to that post and it often answers their question.

maybe we should have a sticky listing these equations.

maybe throw in something about how to draw a spacetime diagram too. and a note about the lines of simultaneity being different for observers moving at different velocities (which as what beginners always have trouble with). anyone know of any good posts for that?